NO. experimental procedures have shown that if you use a laser to distroy the centrioles of an animal cell it will still divide.
Actually, according to Molecular Biology of the Cell a spindle can form with no problems even without centrosomes. It is called a bipolar spindle, and it has provided evidence that chromosomes play an active role in spindle formation...

"As a biologist, I firmly believe that when you're dead, you're dead. Except for what you live behind in history. That's the only afterlife" - J. Craig Venter